SSLC Maths Eng April 2011

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( SPACE FOR ROUGH WORK )

General Instructions :

i) The Question-cum-Answer Booklet consists of objective and subjective types of

questions having 58 questions.ii) Space has been provided against each objective type question. You have to

choose the correct choice and write the complete answer along with its alphabet

in the space provided.

iii) For subjective type questions enough space for each question has been provided.

You have to answer the questions in the space.

iv) Follow the instructions given against both the objective and subjective types of

questions.

v) Candidate should not write the answer with pencil. Answers written in pencil will

not be evaluated. ( Except Graphs, Diagrams & Maps )

vi) In case of Multiple Choice, Fill in the blanks and Matching questions,

scratching / rewriting / marking is not permitted, thereby rendering to

disqualification for evaluation.

vii) Candidates have extra 15 minutes for reading the question paper.

viii) Space for Rough Work has been printed and provided at the bottom of each page.

I. Four alternatives are given for each of the following questions / incomplete

statements. Only one of them is correct or most appropriate. Choose the correct

alternative and write the complete answer along with its alphabet in the space

provided against each question. 20 × 1 = 20

1. If set A = { 2, 3, 4, 5 } and set B = { 4, 5 } then which of the following is a null

set ?

(A) A – B (B) B – A

(C) A U B (D) A I B.

Ans. :

RollNo.

Serial No. of Q. C. A. B.

≤¡ÈJ …Â X‡ Rπ Â›Â ‚Â¢z W : 58

Total No. of Questions : 58

‚Â¢xË∆ Â ‚Â¢z W : 81-E

ê·ÂŒÈ: π Âä∆ ÂCode No. : 81-E

Subject : MATHEMATICS(ß¢ÇYË·˜Ô ü˘ Ê·Ê¢∆ Â¬Â / English Version )

å»Ê¢∑ : 05. 04. 2011 Date : 05. 04. 2011

‚ÂÆÂÈŒÈ : ü úπ B 10-30 à¢«Â ÆÂÈ«˘ ÊW„Â R 1-45 ¬ÂÕÂ¬ π Time : 10-30 A.M. to 1-45 P.M.

…Â¬ÂÆÂ⁄ÕÂå˘ •¢∑π Â›ÂÈ : 100 Max. Marks : 100




2. The Harmonic mean of P and Q is

(A)2 ( P + Q )

PQ (B)2 PQ

P + Q

(C)2 ( P + Q )

P – Q (D)2 P + Q

PQ .

Ans. :

3. If ( AB ) l =

2 3 5 6

then B l A l =

(A)

2 5

3 6

(B)

2 3

6 5

(C)

2 3 5 6

(D)

5 6 2 3

.

Ans. :

4. Which one of the following is a correct relationship ?

(A) n P r

= n C r

∞ r (B) n C r

= n P r

∞ r

(C) n P r

= n C r

÷ r (D) n C r

= n P r

÷ r .

Ans. :

5. Coefficients of variation of price of four foodgrains namely rice, wheat, jowar and

ragi are 10, 11, 13 and 9 respectively. Then which foodgrain’s rate is more

consistent ?

(A) Rice (B) Wheat

(C) Jowar (D) Ragi.

Ans. :




6. H.C.F. of ( )m 2 – n 2 and ( m + n ) 2 is

(A) ( m + n ) (B) ( m – n )

(C) ( )m 2 – n 2 (D) ( m + n ) 2 .

Ans. :

7. Which one of the following is equal to the relation

∑a‚b‚c

a 2 + ∑a‚b‚c

2ab ?

(A) ( a + b ) 2 (B) ( a + b ) 3

(C) ( )a 2 + b 2 + c 2 (D) ( a + b + c ) 2 .

Ans. :

8. When ∑ x‚y‚z

( x + y ) is expanded and simplified, we get

(A) x + y + z (B) 2 x + 2 y + 2z

(C) 3 x + 3 y + 3z (D) 3 xyz.

Ans. :

9. The Algebraic expression having factors ( a + b ) and ( )a 2 + b 2 – ab is

(A) a 3 + b 3 (B) a 3 – b 3

(C) ( a + b ) 3 (D) ( a – b ) 3 .

Ans. :

For More Question Papers Visit http://pediawikiBlog.blogspot.com




VIII I-E-912130 [ Tur

10. If a + b + c = 0, the value of ( b + c ) ( c + a ) is

(A) bc (B) ca

(C) ab (D) abc.

Ans. :

11. When 2 x – y is subtracted from 5 x + 2 y , the answer is

(A) 3 x + 3 y (B) 3 x – y

(C) 3 x + y (D) 3 x – 3 y .

Ans. :

12. An example for pure quadratic equation is

(A) 2 x 2 – x = 0 (B) 5 x = 3

(C) 4 x = 9 x 2 (D) 2 x 2 = 16.

Ans. :

13. If the one of the roots of the equation x 2 – 5 x = 0 is zero, then the other root is

(A) 0 (B) – 5

(C) + 5 (D) ± 5.

Ans. :



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14. If 4a =36a the value of a is

(A) ± 9 (B) ± 3

(C) + 3 (D) – 3.

Ans. :

15. If a and b are the roots of the equation x 2 – 5 x + 7 = 0, then value of

ab ( a + b ) is

(A) 5 (B) 25

(C) 35 (D) 49.

Ans. :

16. Which one of the following groups is a Pythagorian triplet ?

(A) 3, 4, 5 (B) 1, 2, 3

(C) 2, 3, 4 (D) 9, 10, 14.

Ans. :

17. Formula for total surface area of a solid hemisphere is

(A) 4πr 2 (B) 2πr 2

(C) 3πr 2 (D) πr 2 .

Ans. :

18. Area of the base of a circular cylinder is 154 sq.cm and height is 10 cm. The

volume of cylinder is

(A) 1540 c.c. (B) 15·4 c.c.

(C) 164 c.c. (D) 144 c.c.

Ans. :



7 81-E



19. The sum of the order of nodes in the given network is

B

A

C

(A) 3 (B) 4

(C) 8 (D) 10.

Ans. :

20. The numbers of vertices and edges respectively in a Hexahedron are

(A) 8, 12 (B) 12, 8

(C) 6, 8 (D) 8, 6.

Ans. :

II. Complete the following statements by filling in the blanks : 10 × 1 = 10

21. If A and B are disjoint sets then ( A I B ) becomes a ……………………… set.

Ans. :

22. If A is non-zero matrix, then ( ) A l l = ……………………… .

Ans. :

23. The value of n P

0= ……………………… .

Ans. :

24. The conjugate of a x + b y is …………………………… .

Ans. :




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25. The standard form of pure quadratic equation is ………………………… .

Ans. :

26. If m and n are the roots of the quadratic equation ax2

+ bx + c = 0, the sum of the roots m + n is ………………………… .

Ans. :

27. Two circles of radii R and r units, touch externally. The formula for the distance

between the centres, d = ………………………… .

Ans. :

28. Formula for curved surface area of a cylinder is ……………………… .

Ans. :

29. The Euler’s formula for graph is ………………………… .

Ans. :

30. In the following figure if AP = 3 cm and PC = 8 cm, length of the tangent CD

is …………………………… .

D

C

B

P

A

3 cm

8 c m

Ans. :



9 81-E



III. Solve the following problems in the space provided : 18 × 2 = 36

31. If ∑ n = 210, find the value of n.

32. A person deposits Rs. 1,000 in the first month. Then every month he increases

the monthly deposit by Rs. 60. Use the principle of progression and calculate his

total investment at the end of two years.




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33. If A.M. and H.M. of two numbers are 10 and 6·4 respectively, find Geometric

mean.

34. If A =

3 – 2 4 2

, show that A + A l is a symmetric matrix.



11 81-E



35. If 5 n P

3= 4 ( n + 1 )

P3

, find the value of n.

36. A school has 8 teachers. How many committees of 5 can be formed ?




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37. Find the H.C.F. of m 3 + 2m 2 + 2m + 1 and m 2 + 2m + 1, by division method.

38. 2 ( )a 2 + b 2 = ( a + b ) 2 , show that a = b.



13 81-E



39. Solve the equation by using formula

x 2 – 5 x + 6 = 0.

40. The perimeter of a rectangular field is 54 metres and its area is 180 sq.m. Find

the length and breadth of this field.




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41. For what values of m the roots of the equation x 2 + mx + 4 = 0 are equal ?

42. If Q = { 0, 2, 4, 6 } under ( ≈ mod 10 ), construct a Cayley’s table.



15 81-E



43. Construct tangents to a circle of radius 3 cm from a point 7 cm away from the

centre.




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44. A trapezium ABCD has its sides AB | | CD and its diagonals intersect at O. If side

AB is twice the side CD, find the ratio of the area of triangle AOB to the area of

triangle COD.

B

C

O

D

A



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45. In the figure, the sides of a quadrilateral ABCD are tangents to the circle with

centre O. Show that AB + CD = AD + BC.

O

R

Q

C

B P

A

D

S




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46. The radius of a cone is 7 cm and slant height is 10 cm. Find the total surface

area of the cone.



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47. Draw a plan for the recordings from the surveyor’s field book given below.

( Scale : 20 m = 1 cm )

( Metres )To C

220

To D 100 180 H

120 G 100 to B

To E 140 80 F

From A




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48. Draw the graph for the matrix

0 2 2 2 0 1 2 1 0



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IV. 49. (a) In a class of 60 students, everyone should select Mathematics or Science or

both. If 45 students select Mathematics, 30 students select Science, how

many students did select both the subjects ?

(b) Draw a Venn diagram. 3




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50. Calculate the Arithmetic mean and Standard deviation for the given frequency

distribution : 3

Class-interval Frequency

1 – 5

6 – 10

11 – 15

16 – 20

2

3

4

1

N = 10



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51. Find the L.C.M. of expressions a 3 – 3a 2 – 10a + 24 and a 3 – 2a 2 – 9a + 18 by

division method. 3




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52. Rationalise the denominator and simplify : 3

3 2

6 – 3+

4 3

6 + 2



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53. The height of an equilateral triangle is 5 3 cm. Find its perimeter. 3




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54. Prove that the tangents drawn to a circle from an external point are

(i) equal

(ii) equally inclined to the line joining the external point and the centre. 3



27 81-E



V. 55. The sum of three numbers of a G.P. is 57 and their product is 343. Find the

numbers. 4




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56. Draw two circles of radii 4 cm and 2 cm with their centres 10 cm apart. Draw the

transverse common tangent ( T.C.T. ) to them and measure the length of the

tangent. 4



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57. Prove that if two triangles are equiangular, then their corresponding sides are

proportional. 4




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58. Draw the graphs of y = x 2 and y = 2 x + 3 and hence solve the equation

x 2 – 2 x – 3 = 0. 4



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SSLC Maths Eng April 2011

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